Магистратура
2023/2024
Линейная алгебра
Статус:
Курс обязательный
Направление:
01.04.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
1-й курс, 3 модуль
Формат изучения:
с онлайн-курсом
Онлайн-часы:
52
Охват аудитории:
для своего кампуса
Преподаватели:
Медведь Никита Юрьевич
Прогр. обучения:
Магистр по наукам о данных (о)
Язык:
английский
Кредиты:
3
Контактные часы:
10
Course Syllabus
Abstract
Linear algebra provides arithmetic and algebraic operations which can be applied to large arrays of data. These operations are in the core of the most methods of data analysis.
In this course, we discuss the most important linear algebra concepts and algorithms. Then we use this theory to treat a serious data analysis case. Each topic of our course contains theory, numerical examples, and examples of programming using Python.
In the final project, you will develop a python software for recognizing hand-written digits.
Learning Objectives
- The aim of the course is to provide the theoretical background of solutions to linear algebra problems which appear in data analysis and machine learning.
Expected Learning Outcomes
- Able to find the solution of a system of linear equations using Gaussian elimination
- Able to calculate LU and PLU decompositions
- Able to calculate and use full rank decompositions
- Able to use the linear regression model to make simple prognoses
- Able to use the Gram-Schmidt method for the orthogonalization
- Able to find the characteristic polynomials and the eigenvalues of a matrix
- Able to calculate and use SVD decomposition
- Able to implement the above methods in Python for machine learning solutions
Course Contents
- 1. Systems of linear equations and linear classifier
- 2. Full rank decomposition and systems of linear equations
- 3. Dimensionality reduction
- 4. Linear operators and walks on graphs
- 5. Distances and operators in Euclidean space
- 6. Singular value decomposition (SVD) and Principal Component Analysis (PCA)
Assessment Elements
- QuizzesEvery week contains a graded quiz. For each quiz, you have 2 attempts. Please note, that some lessons have ungraded quizzes with similar tasks to help you practice.
- SGAWeek 3 and 6 contain Staff Graded Assignments (SGAs): "SGA Week 3" and "SGA Week 6". They are manually evaluated by teaching staff. SGAs have strict deadlines. You can submit your answers to an SGA only once.
- Final ProjectThe final project consists of two parts: programming qualitative tasks and qualitative questions.
Bibliography
Recommended Core Bibliography
- Anthony, M., & Harvey, M. (2012). Linear Algebra : Concepts and Methods. Cambridge, UK: Cambridge eText. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=443759
- Williams, G. (2019). Linear Algebra with Applications (Vol. Ninth edition). Burlington, MA: Jones & Bartlett Learning. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1708709
Recommended Additional Bibliography
- Anton, H. (2014). Elementary Linear Algebra : Applications Version (Vol. 11th edition). Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1639248